fugitivity to interpretation t

an apologetic postscript

because” and “despite” coexists

his thesis keeps many of our inside jokes and meme

Hermocrates

this section is nothing less than theseimpossible acts of longing for the ineffable

nonexistent summit of Aetna where Hölderin’sEmpedocle

Acknowledgements

first, that as the race climbs higher in the scale of development, sodevelopment shall proceed at an accelerated pace; second, that in the same proportion, the race shallbecome less fertile.

Workmenare annually consumed, and fresh ones introduced

and by him it is handed down on his death-bed to none buthis Successor

Under the skillful generalship of the Circles almostevery Woman's charge was fatal and very many extracted their sting uninjured, ready for a secondslaughter.

Manyof them, he said, were on the point of being admitted to the class of the Regular Triangles; othersanticipated for their children a distinction they could not hope for themselves. That honourable ambitionwould now have to be sacrificed.

Colour Bill

The Art of Sight Recognition

we are even now indebted for our finest poetry and forwhatever rhythm still remains in the more scientific utterance of these modern days.

infant whose angle deviates by half a degree from the correct angularity is summarily destroyedat birth

I for my part havenever known an Irregular who was not also what Nature evidently intended him to be - a hypocrite, amisanthropist, and, up to the limits of his power, a perpetrator of all manner of mischief

more than, a combination of moral obliquity and criminality with you, and istreated accordingly

For this reason, among our Higher Classes, ``Feeling'' is discouraged or absolutely forbidden. From thecradle their children, instead of going to the Public Elementary schools (where the art of Feeling istaught,) are sent to higher Seminaries of an exclusive character; and at our illustrious University, to``feel'' is regarded as a most serious fault, involving Rustication for the first offence, and Expulsion forthe second

the cheap system

Mr.Smith, permit me to feel Mr. Jones.

The tact and skill which suffice to avert a Woman's sting are unequal to thetask of stopping a Woman's mouth; and as the wife has absolutely nothing to say, and absolutely noconstraint of wit, sense, or conscience to prevent her from saying it, not a few cynics have been found toaver that they prefer the danger of the death-dealing but inaudible sting to the safe sonorousness of aWoman's other end

jealousies and suspicions skilfully fomented among them by the Circularparty, they are stirred to mutual warfare, and perish by one another's angles

to make some of the more intelligent leaders of a rebellionperfectly Regular, and to admit them at once into the privileged classes

And how perfect a proof of the natural fitness and, I mayalmost say, the divine origin of the aristocratic constitution of the States in Flatland!

in proportion as the working-classes increase in intelligence, knowledge, and allvirtue, in that same proportion their acute angle (which makes them physically terrible) shall increasealso and approximate to the comparatively harmless angle of the Equilateral Triangle.

while they do little or nothing to vulgarize their own privileges, serve as a most usefulbarrier against revolution from below

for fear lest the freshly developed organism may, by force of unconsciousimitation, fall back again into his hereditary level.

of the coming Equilateral, and a patient, systematic, and continuousdevelopment of the Isosceles intellect through many generations

But, writing as a Historian, he has identified himself(perhaps too closely) with the views generally adopted by Flatland, and (as he has been informed) evenSpaceland, Historians; in whose pages (until very recent times) the destinies of Women and of the massesof mankind have seldom been deemed worthy of mention and never of careful consideration.

One touch of Nature makes all worlds akin

lt has been objected that he is awoman-hater

even I cannot now comprehendit, nor realize it by the sense of sight or by any process of reason; I can but apprehend it by faith.

Most biologists believe that P =(0),anda biomathematical argument exists for this claim

In order to decide which is the biologically correct solution, we mustutilize more experimental evidence

biologists prefer to use gel electrophoresisasthe assay from which experimental conclusions are to be drawn

(Wasserman et al., 1985)

<2,1,1>

parental tangleP is removed from the synaptosome and replaced by the recombinanttangleR

Mostofthese assumptions are implicit in theexisting analysesofthe resultsofenzyme experiments on circular DNA

Figure 8.7 shows some standard tanglediagrams

DNA is bound to thesurfaceofthe protein. This means that the resulting protein-DNA tangleis rational, since any tangle whose strings can be continuously deformedinto the boundaryofthe defining ball is automatically rational

A class of equivalent tangles is called a tangle type.

On the unit 3-ball, select four points on the equator (called NW,SW, SE, NE)

boundary 2-sphere 8 2 = oB 3

Standard 4-plats

plectonemic supercoiling

well-understood familyof4-plats

that uniquely classifycertain homologous subfamiliesofknots and links, for example, torusknots, two-bridge knots (4-plats), and so on.

insisted that thetransformation that superimposes one knot on another must beorientation-preserving on the ambient space.

tum up in Tn3 recombinationexperiments

An equivalence classofembeddings is called a knot (link) type

dimers, that is, linksoftwo components, because dimers are the onlylinks that tum up in topological enzymology experiments

describe the partsofknot theory and tanglecalculusofbiological relevance

RecA-coated DNA is approxi-mately 100 angstroms in diameter

higher thecrossing number, the greater the gel mobility

surprisingly) determined by the crossingnumberofthe knot or link

reaction products prior toelectrophoresis in order to relax the supercoils in the DNA knots andlinks

perform recombination in multiple binding encounters with the DNA,which is called distributive recombination.

deduce mathematically the path of theDNA in the black mass of the synaptosome, both before and afterrecombination

synaptic complex

nzyme thatmediates site-specific recombination on DNA is called a recombinase

Site-specific recombination

At this point they can be examined and dissected

entangled formofthe product DNA knotsand links contains information about the enzymes that made them.

figure eightcatenane

black box

catenanes

passing onestrandofDNA through another by meansofa transient enzyme-bridgedbreak in oneofthe DNA strands

Ifone scales the cell nucleus up to the sizeofa basketball, theDNA inside scales up to the sizeofthin fishing line, and 200 kmofthatfishing line are inside the nuclear basketball

The three-dimensional shape insolution isof great biological significance but is very difficult todetermine

in solution in the cell

two theorems

topological results about knots and tangles

aspectoftopoisomerases is dealt with in more detail in Chapter8

rather a supercoiled DNA with linking number differenceof-25

mixtureofthe same DNA with linking numberdifferences that vary all the way from the original number to0

linking number differenceofa supercoiled DNA can be reduced to 0

distributed to change the average twist by +0.28 and the average writheby +0.72 in accordance with the results mentioned abov

enzymes were found that can actually change the linking numberdifference

supercoiled

or each changeof1 in the linking difference, there is a changeof0.72 in the writhe

writheofa planar curve is 0

in most cases is less thanLk0

heavilyused telephone cord

After some time, muchofthe twisting will be seen to introducewrithingofthe axisofthe elastic material

closed strand of DNAofconstant linking numbe

Lk=Tw+Wr

When A is a straight line segment or planar curve,dv.<always isperpendicular to the curve A, so that in these cases, Tw reduces to thenumberoftimes thatv.cturns around the axis

we need the use of vector

White, J.H., and W.R. Bauer, 1986, "Calculation of the twist and the writhe forrepresentative models of DNA," Journal of Molecular Biology 189, 329-341.

two distant segmentsofa DNA axisare brought very close together, then this proximity will contributeapproximately±1to the writhing number because in almost all viewsthis proximity will be seen as a crossing.

writhing numberisdefined as the average over all possible viewsofthe projected writhing number

helical windingofthe backbone curve around theaxis

DNA axis is seen to cross itself,

writheWrand twist Tw,which can be used to describe supercoiling (White, 1969)

For a relaxed circular DNA moleculeofthe monkey virus SV40,which has approximately 5,250 base pairs,Lkis about 500, and forbacteriophage Aofabout 48,510 base pairs,Lkis about 4,620

does not depend on theprojection or viewofthe pair

one adds allofthe signed numbers associated with thisprojection and divides by 2, one obtains the linking numberofthe curvesA and C,Lk(A,C)

Such a viewgives a modified projectionofthe pairofcurve

topologyofknot theory to explain the actionofenzymes in carrying out the fundamental processofsite-specificrecombination.

Lk(R) = T w(R) + W r(R).

ormula for the sum ofthe first a + 1 terms of a geometric series with ratio p

Since the arithmetic function f(d) = d is multiplicative (verifythis!), we have that u(n) is multiplicative by Theorem 3.1

disjointness of sub-graphs in G′ ensures that these paths do not cycle

each node in the coregraph has degree either zero or two

ode has two incident edges

node is isolated in G′ and has degree zero

e1, e2, e3,and e4 belong in E

edge to belong in E′only if it lies between a X-face and an O-face

If every tile of the Hex board is markedeither x or o

u and v now have degree at most 1 since they had degree atmost two before we removed edge (u, v)

all the nodes are isolated

Each node can have degree at most two, so g can haveat most N edge

supercoiling helps incellular packaging of DNA in structures called nucleosomes, in whichDNA is wound around proteins called histones

cruciforms

polyrnerases

helicases

Supercoiling of closed DNA is ubiquitous in biological systems

may, in general, assume almostany configuration in space

xis ofthe double helix may itself be a helix

commonlinear axis

fundamental theorem

Figure 18

return to itsnatural twist rate,

linking number of the ribbon is equal to the linkingnumber of this link

average signed crossover number over all possible projections of the ribbon inspace

Definition 2.3

duplex DNA

tangles

S = (-3, 0)and R = (1)

substrate molecule as N (S + T ) and the product molecule as N (S + R)

knot Q

substrate molecule (the molecule before the enzyme acts)

circular (cyclic) DNA

several more general action

projections

measure of howintertwined two components of a link are

linking number

new terminol-ogy, writhe, to model this type of cyclic DNA.

examples of your ow

explanations of proof ideas or important results if relevant

10access to the shared resources. In addition, it only considers a singleprocessor and ignores the overhead caused in changing the mode. In thefuture, we will focus on scheduling energy aware dependent periodictasks in multiprocessor MC real-time systems with the overhead ofchanging the mode

reduce energy consumption up to 32.45 and46.84% compared with Algorithm A in the normal mode and urgencymode, respectively

Effect of the ratio of Ci (LO)Ai (L

energy consumption up to 32.45% in the urgency mode

herefore, EAU can reduce energy consumption up to41.63%

can reduce energy consumption up to 21.17%

normalized energy consumption when ULOLO(Γ) was equal to 0.45

In addition, the ratio of Ci(LO) and Ai(LO) was set to 5 for any task τi.

1.3

ULOHI (Γ)

Effect of UHIHI (Γ)

Therefore, EAU can reduce energy consumption up to 46.30% inthe urgency mode compared with Algorithm A as shown in Fig. 9(b).

actualexecution time of tasks

pplied the uniform distribution method to select theparameter of the task

slack time generated from the early completion jobs and the jobswere executed with Shigh in the urgency mode.

HI level task is executed with Smax in the urgencymode

rocessor could providediscrete normalized speed levels, i.e., [0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,1.0]

That is Pind = 0.1, Pmaxdynamic was normalized to 1 and θwas set to 0.2 in Eq. (1) [2]

Pind = 0.1, Pmaxdynamic = 1 and θ = 0.2

Case 3: EAU is feasible in a changed mode

sum utilization of tasks

asks are put intothe delay queue

other is a delay queue that in-cludes the unreleased and completed job

If the HI level job τijends and its execution time exceeds Ci(LO)/S under S, the system willswitch to the urgency mode

Smax

Algorithm A computes the parameter x= 0.875, the optimal speed of LO tasks SLO = 0.86, and the optimal speedof HI tasks SHI = 0.90

Ci(LO) ≤ Ai(HI)

When the HI level task is not completed on time and its execution timeexceeds the worst case execution time (WCET) in the normal modeunder the processor speed S

If ζ = LO, then the virtual deadline of τi is assigned to ti + T

Wederived the energy model parameters from the state-of-the-art researches in this area [24], [28], [29], [37], [38]. Weassumed thatmaxdynamicP is normalized to 1 and0.1

Static and dynamicpower components can be reduced by selecting lowerivalues for a task

)dynamicmaxi ind i i

I

optimal x is 0.625 where f HIand f LO are 0.7 and 0.5 in each

urrently-executing job executes for more than itsLO -criticality WCET without signaling completion

ob is assigned a scheduling deadlineequal to t + ˆTi

lies somewhere within the interval

x U LOLO (τ ) + U HIHI (τ ) ≤ 1

sufficientcondition for ensuring that EDF-VD successfully meets allHI -criticality deadlines during all HI -criticality behaviors ofτ

x ← U LOHI (τ )1 − U LOLO (τ )

ll currently-active LO -criticality jobs are immediately dis-carded; henceforth, no LO -criticality job will receive anyexecution

ta + ˆTi

ta + Ti

Ti ≤ Ti

τ

U yx (τ ) =∑τi ∈τ ∧χi =xCi(y)Ti

all HI -criticality jobs receive enough execution between their releasetime and deadline to be able to signal completion.

Each such job has a deadline that is Tk time unitsafter its release.

erroneous behavior

if evenone job Ji signals completion after executing for more thanci(LO) but no more than ci(HI) units of execution, we saythat the system has exhibited HI-criticality behavio

γi

sporadic

run-timecomplexity per scheduling decision was logarithmic in thenumber of task

[8]

Integrated Modular Avion-ics (IMA) [19] in aerospace and AUTOSAR

Mawhin, J. (2007). Le th ́eor`eme du point fixe de Brouwer: un si`ecle de m ́etamorphoses.Sciences ettechniques en perspective10(2): 175–220.